Orthomodular lattices can be converted into left residuated l-groupoids

@article{Chajda2017OrthomodularLC,
  title={Orthomodular lattices can be converted into left residuated l-groupoids},
  author={Ivan Chajda and Helmut Langer},
  journal={Miskolc Mathematical Notes},
  year={2017},
  volume={18},
  pages={685}
}
We show that every orthomodular lattice can be considered as a left residuated l-groupoid satisfying divisibility, antitony, the double negation law and three more additional conditions expressed in the language of residuated structures. Also conversely, every left residuated l-groupoid satisfying the mentioned conditions can be organized into an orthomodular lattice. 
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